Boundary actuation structure of linearized two-phase flow

In this paper, we introduce a two-phase flow model which describes the motion of two incompressible fluids. The proposed model is governed by nonlinear partial differential algebraic equations (PDAEs) with open initial-boundary conditions. The well-posedness of the boundaries is analyzed using characteristic curves, which leads to development of a boundary actuation structure that is suitable for a control design. A particular emphasis is placed on a possible coordinate transformation that can reduce the problem to a set of partial differential equations (PDEs) without algebraic constraints. The boundary actuation strategy is presented using linearized model equations and tested on a numerical example for a quasi steady-state situation.